All categories

3 years ago

What is the value of x? sin(x + 22)° = cos(2x - 7)º

Mathematics

2 answers:

Contact [7]3 years ago

6 0

Answer:

x = 25

Step-by-step explanation:

Recall the trig identity sin(x) = cos(90 - x)

In other words, sin(x + 22) = cos(90 -(x+22)) = cos(68 - x)

Now, set them equal to each other:

cos(68 - x) = cos(2x - 7)

We can ignore the cosine:

68 - x = 2x - 7

3x = 75

x = 25

EleoNora [17]3 years ago

5 0

Answer:

x=25°

Step-by-step explanation:

sin (x+22)=cos(2x-7)=sin (90-(2x-7))

x+22=90-(2x-7)

x+22=90-2x+7

x+2x=97-22

3x=75

x=75/3=25°

You might be interested in

Which of the following values of x make the following functions equal? y = 2x + 6 and

Papessa [141]

Answer:

the answers Is c. x=4

Step-by-step explanation:

do substitution 2*4+6=14

and 6*4-10=14

6 0

2 years ago

Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

4 0

1 year ago

A right rectangular prism has a length of 10 centimeters, a width of 2.5 centimeters and a height of 0.9 centimeters what is the

nikdorinn [45]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{22.5 \: {cm}^{3} }}}}}$

Step-by-step explanation:

Given,

Length of a rectangular prism ( l ) = 10 cm

Width of a rectangular prism ( w ) = 2.5 cm

Height of a rectangular prism ( h ) = 0.9 cm

Volume of a rectangular prism ( V ) = ?

Finding the volume of a rectangular prism

$\boxed{ \bold{ \sf{volume \: of \: a \: rectangular \: prism = lwh}}}$

$\dashrightarrow{ \sf{volume = 10 \times 2.5 \times 0.9}}$

$\dashrightarrow{ \sf{volume = 22.5 \: {cm}^{3} }}$

Hope I helped!

Best regards! :D

7 0

3 years ago

Jake plans to use a ramp to make it easier to move a piano out of the back of his truck. the back of the truck is 333333 inches

Anastaziya [24]

736334.49 inches
if the measurements given are 333333 and 656565 then to find the diagonal length. we can use the Pythagorean theorem.
333333^2 + 656565^2 = x
take the square root of 333333^2 + 656565^2 to get 736334.49

6 0

3 years ago

Read 2 more answers

Can someone help me with this one

Mkey [24]

Answer:

The answer is 1/10. Mark as brainliest ^-^

Step-by-step explanation:

8 0

3 years ago