World and Nation

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U.S. economy grew at brisk rate in second quarter

The U.S. economy grew faster than first thought last quarter, the Commerce Department said Thursday, the latest in a series of signals that suggest a period of sustainable growth lies ahead.

Increased investment by businesses and a slightly improved trade picture prompted the revision, which lifted the estimated annual rate of growth in April, May and June to 4.2 percent from the government’s initial reading of 4 percent in late July.

Since the economy emerged from the recession five years ago, companies have been hesitant to spend heavily on new capacity, but these figures and other recent data indicate that is finally changing.

—Nelson D. Schwartz, The New York Times

Teacher accused of sending lewd photo

NEW YORK — A Brooklyn high school teacher was arraigned Tuesday on charges that he sent a sexually explicit photograph to a student over the popular messaging app Snapchat.

The teacher, Sean Shaynak, 44, of East Flatbush, teaches math and science at Brooklyn Technical High School, the Brooklyn district attorney’s office said. He was arrested on Tuesday and arraigned in state Supreme Court in Brooklyn on charges of disseminating indecent material to a minor, obscenity, endangering the welfare of a minor and harassment.

Prosecutors said he sent a photo of his genitals to a 16-year-old female student over Snapchat on June 27. The service allows users to send messages that disappear after a few seconds, but the student kept the image by photographing it with her cellphone.

The student, who was a friend of Shaynak’s on Facebook, told an adult about the incident, and they reported it to the FBI, prosecutors said.

The teacher was reassigned immediately and will not be in contact with students, said Devora Kaye, a spokeswoman for the New York City Department of Education.

“This alleged behavior is unacceptable and has no place in our schools,” Kaye said in a statement.

Shaynak was held in lieu of $100,000 bond or $25,000 cash. He could face up to seven years in prison if he is convicted, prosecutors said. His lawyer, Howard Kirsch, did not respond to a request for comment.

Kenneth P. Thompson, the Brooklyn district attorney, said in a statement, “This is a disturbing allegation as schools should be safe havens for students where teachers should protect our children from, and not expose them to, such disgusting sexual images.”

—Emma G. Fitzsimmons, The New York Times

Shell submits a plan for new Alaskan arctic oil exploration

After years of legal and logistical setbacks and dogged opposition from environmentalists, Royal Dutch Shell submitted a plan to the federal government Thursday to try once again to explore for oil in the Alaskan Arctic.

The company emphasized that it had not made a final decision on whether to drill or not next summer, but that the filing with the Interior Department preserved its options. Shell says the program consists of two drilling rigs working simultaneously in the Chukchi Sea, which has the potential to produce more than 400,000 barrels of oil a day.

Over the last eight years Shell’s Alaskan Arctic efforts have been plagued by blunders and accidents involving ships and support equipment, climaxing with the grounding of one of its drilling vessels in late December 2012 in stormy seas. Environmental groups seized on the episodes as evidence to support their claims that drilling in the Arctic is overly risky because of ice floes, darkness in winter and the presence of several species of threatened wildlife, including polar bears.

The company, which has spent roughly $6 billion on the effort, drilled two shallow wells in Alaska’s Arctic during 2012. But the federal government did not allow Shell to reach the deeper, oil-bearing formations; the company did not have the required ability to contain spills after the testing failure of a containment dome designed to cap a runaway well and collect oil in case of an accident.

—Clifford Krauss, The New York Times

$506 billion is forecast for deficit, a slight rise

WASHINGTON — The federal government is expected to finish its fiscal year with a relatively modest budget deficit as the gap between revenue and spending continues a sharp decline, the Congressional Budget Office said Wednesday.

The improvement in the government’s financial health has shifted political debate in Washington, and arguments on the midterm campaign trail, from the level of federal spending to the uses of that money. It has frustrated economists who argue that the government’s restraint has held back the economic recovery.

The budget office said that it now predicted a federal deficit of $506 billion during the fiscal year that runs through the end of September, modestly increasing its April projection that spending would exceed revenue by $492 billion. The change was attributed to lower-than-expected corporate income tax receipts.

Both figures are significantly lower than the $680 billion deficit during the previous fiscal year.

The budget office also said it expected somewhat smaller deficits in coming years, reducing the accumulation of the federal debt by about $400 billion in the next decade. The projection largely reflects an expectation that the government will be able to borrow at lower interest rates.

The budget office’s projection earlier this year was criticized by some analysts for assuming the government would face an unlikely combination of slow economic growth and high rates.

The fiscal outlook also has benefited from a decline in projected Medicare spending.

—Binyamin Appelbaum, The New York Times